Inequalities for norms of derivatives of non-periodic functions with non-symmetric constraints on higher derivatives

V.A. Kofanov (Oles Honchar Dnipropetrovsk National University),


For non-periodic functions $$$x \in L^r_{\infty}(\mathbb{R})$$$ defined on the whole real line we established the analogs of certain inequality of V.F. Babenko.


inequalities for derivatives; non-symmetric norms


Ligun А.A. "Inequalities for upper bounds of functionals", Analysis Math., 1976; 2(1): pp. 11-40.

Babenko V.F. "Non-symmetric extremum problems of approximation theory", Dokl. AN SSSR, 1983; 269(3): pp. 521-524. (in Russian)

Bojanov B., Naidenov N. "An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös", Journal d'Analyse Mathematique, 1999; 78: pp. 263-280.

Kofanov V.A. "Exact upper bounds of norms of functions and their derivatives on the classes of functions with given comparison function", Ukrainian Math. J., 2011; 63(7): pp. 969-984. (in Russian)

Pinkus A., Shisha O. "Variations on the Chebyshev and $$$L^q$$$-Theories of Best Approximation", Journal of Approx. Theory, 1982; 35(2): pp. 148-168.

Hörmander L. "A new proof and generalization of inequality of Bohr", Math. Scand., 1954; 2: pp. 33-45.

Babenko V.F., Kofanov V.A., Pichugov S.A. "Inequalities of Kolmogorov Type and Some Their Applications in Approximation Theory", Rendiconti del Circolo Matematico di Palermo. Serie II, Suppl., 1998; 52: pp. 223-237.

Korneichuk N.P., Babenko V.F., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Nauk. dumka, Kyiv, 2003; 590 p. (in Russian)

Kofanov V.A. "Some exact inequalities of Kolmogorov type", Mat. fizika, analiz, geometriya, 2002; 9(3): pp. 1-8.




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